Let

1 = A(x⁴ + 1) + (Bx³ + Cx² + Dx + E)(x)

Equating constants

A = 1

Equating coefficients of x⁴

0 = A + B

0 = 1 + B

B = – 1

Equating coefficients of x²

D = 0

Equating coefficients of x

E = 0

Thus,